This research addresses the Vehicle Routing Problem (VRP) with uncertain data and proposes a novel approach using quantum computing techniques. The problem involves optimizing vehicle routes considering uncertain customer demands, time windows, and vehicle capacities. We formulate the problem mathematically and develop an algorithmic framework to tackle it. The approach incorporates multiple scenarios based on the uncertainty distribution and selects the one with the minimum cost to optimize the vehicle routes. Through a numerical example, we demonstrate the effectiveness of the proposed approach in generating optimal routes that minimize the total distance traveled by the vehicles. The results highlight the solution quality, adaptability to uncertainty, and potential benefits in terms of cost reduction and resource utilization. While the computational efficiency of quantum computing approaches is a consideration, this research provides a promising direction for addressing uncertain optimization problems in logistics and transportation. Future research should focus on scalability and refinement of the algorithm to further enhance its applicability in real-world scenarios.
This research addresses the Vehicle Routing Problem (VRP) with uncertain data and proposes a novel approach using quantum computing techniques. The problem involves optimizing vehicle routes considering uncertain customer demands, time windows, and vehicle capacities. We formulate the problem mathematically and develop an algorithmic framework to tackle it. The approach incorporates multiple scenarios based on the uncertainty distribution and selects the one with the minimum cost to optimize the vehicle routes. Through a numerical example, we demonstrate the effectiveness of the proposed approach in generating optimal routes that minimize the total distance traveled by the vehicles. The results highlight the solution quality, adaptability to uncertainty, and potential benefits in terms of cost reduction and resource utilization. While the computational efficiency of quantum computing approaches is a consideration, this research provides a promising direction for addressing uncertain optimization problems in logistics and transportation. Future research should focus on scalability and refinement of the algorithm to further enhance its applicability in real-world scenarios.
In the ever-evolving landscape of global trade and supply chain management, logistics optimization stands as a critical challenge. This study takes on the Vehicle Routing Problem (VRP), a variant of the Traveling Salesman Problem (TSP), by proposing a novel hybrid solution that seamlessly combines classical and quantum computing methodologies. Through a comprehensive analysis of our approach, including algorithm selection, data collection, and computational processes, we provide in-depth insights into the efficiency, and effectiveness of our hybrid solution compared to traditional methods. The results after analysis of 14 datasets highlight the advantages and limitations of this approach, demonstrating its potential to address NP-hard problems and contribute significantly to the field of optimization algorithms in logistics. This research offers promising contributions to the advancement of logistics optimization techniques and their potential implications for enhancing supply chain efficiency.
The Vehicle Routing Problem (VRP) is a crucial combinatorial optimization problem in transportation, logistics, and supply chain management. Quantum computing has gained interest in solving complex optimization issues. This review paper proposes a novel approach that combines quantum computing principles with the Feynman path integral formulation to address the VRP. The paper focuses on limited qubits and how quantum algorithms can circumvent this limitation. Conventional methods, such as Lagrangian and combinatorial optimization, require computational time to solve complex atomic-scale problems. The path integral formulation with the first Born approximation method offers a more elegant explanation of quantum computing. The algorithm investigates quantum system dynamics using the Schrodinger wave equation and computes probability amplitude distributions for optimal vehicle routing techniques. This work will take advantage of entanglement and interference effects for heuristic sampling of high-quality solutions, making the Quantum Path Integral Approach (QPIA) a promising study environment for investigating quantum circuits and algorithms in routing problems with constrained qubits.
In the current competitive industrial environment, the study of NP-hard issues is becoming more and more significant. In logistics, the Vehicle Routing Problem (VRP) is one of the popular challenges, especially in cold chain logistics, which requires the management of perishable goods. This problem involves identifying the optimal paths for vehicles responsible for transporting goods to different locations. Due to its combinatorial nature and the complexity of finding optimal solutions, it is identified as an NP-hard problem that requires an unreasonable time frame to solve. Recently, quantum computing has proven to be a promising approach for addressing some of the complex challenges. Among quantum methodologies, quantum annealing (QA) has demonstrated the potential to accelerate computation times in solving optimization problems. By leveraging the principles of quantum tunneling and superposition, QA can explore solution spaces more efficiently. Therefore, this study explores the application of QA to address VRP in cold chain logistics, aiming to develop solutions that minimize travel distances during deliveries. The case study demonstrates that QA can achieve, on average, at least 85% of optimal performance while providing approximately 95% faster run times compared to classical genetic algorithms (GA). This contributes to greater efficiency in cold chain logistics operations.
Current world trade is based and supported in a strong and healthy supply chain, where logistics play a key role in producing and providing key assets and goods to keep societies and economies going. Current geopolitical and sanitary challenges faced in the entire world have made even more critical the role of logistics and increased demands for tuning transport function to keep the supply chain up and running. The challenge is only increasing and growing for the future, thus tackling transport optimization provides both business and social value. Optimization problems are ubiquitous and they present a challenge due to its complexity, where they're typically NP-hard problems. Quantum Computing is a developing field, and the Quantum Annealing approach has proven to be quite effective in its applicability and usefulness to tackle optimization problems. In this work we treat the Vehicle Routing Problem, which is also a variation of a famous optimization problem known as the Traveling Salesman Problem. We aim to tackle the vehicle optimization problem from the last mile logistic scenario application, with a perspective from the classical and quantum approaches, and providing a solution which combines both, also known as hybrid solution. Finally, we provide the results of the analysis and proposal for the consideration of applications in a near term business case scenario.
The Vehicle Routing Problem (VRP) is a fundamental combinatorial optimization challenge with broad applications in logistics and transportation. In this work, we present a quantum-assisted framework that integrates the Quantum Approximate Optimization Algorithm (QAOA) with a link-based formulation of VRP. Our approach encodes flow conservation and subtour elimination directly into the cost Hamiltonian, preserving graph structure while minimizing resource requirements for practical hardware implementation. We design and implement the full pipeline on a gate-based quantum computer, including problem formulation, encoding, circuit synthesis, and execution on IBM Quantum System One. Experimental results on small VRP instances highlight the effects of penalty scaling, coefficient normalization, and circuit depth on solution feasibility under hardware noise. While scalability remains constrained by circuit complexity and decoherence, the study demonstrates a practical pathway for implementing VRP on quantum hardware and identifies methodological directions for advancing near-term quantum optimization.
Vehicle Routing Problem (VRP) is considered one of the most challenging problems with application in several domains, including transportation and logistics distribution. VRP is known to be NP-Hard problem. Several algorithms have been proposed to solve VRP in polynomial time. However, these algorithms are inefficient if the VRP instance increases. Recently, researchers investigated how quantum computing can be used to solve VRP. In particular, two promising variational quantum algorithms have been studied, i.e., Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA). In this paper, we implement both algorithms on IBM Qiskit and compare their evaluation in solving several instances of VRP. We observe that current Noisy-Intermediate Scale Quantum (NISQ) devices cannot solve VRP instances beyond 5 nodes and 2 vehicles. Furthermore, we observe that classical optimizers still provide better results. However, we believe that with the rapid advancement of quantum computing manufacturing, VQE and QAOA can provide better performance as compared to classical computing,